List questions from artinian

Published on 12 Jan 2021 - 11:08

46

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A non-cyclic Artinian module has at least two distinct minimal (simple) submodule.

Published on 30 Jan 2021 - 18:43

421

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Commutative Artinian ring with infinitely many ideals.

Published on 04 Feb 2021 - 12:03

213

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Cohen structure theorem for Artinian local ring

Published on 08 Feb 2021 - 20:04

89

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Is $(\Bbb Q[x])_x/(\Bbb Q[x])$ an Artinian $(\Bbb Q[x])$-module?

Published on 10 Feb 2021 - 12:56

128

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Noetherian and Artinian quotient

Published on 14 Feb 2021 - 11:32

68

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Do Artin rings contain many commutative Artin subrings?

Published on 02 Mar 2021 - 20:34

70

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Is there exist a hollow module which is not Artinian

Published on 03 Mar 2021 - 5:36

23

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Show that if $P_n$ is a descending chain of submodules in $N$, then so is $f^{-1} (P_n)$ in $M$

Published on 06 Apr 2021 - 21:03

84

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Show that, given $f:M→N$, if M is an artinian module so is N

Published on 06 Apr 2021 - 23:09

51

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$A/\alpha$ is Noetherian as an $A$-module but how to get it is Noetherian as an $A/\alpha$-module?

Published on 19 Apr 2021 - 9:18

114

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Show that $A\simeq k[x_1,...,x_d]/I$

Published on 01 May 2021 - 16:31

152

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Zero dimensional quotient of a local Noetherian ring

Published on 02 May 2021 - 17:22

142

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Question about simple module over semisimple Artinian ring

Published on 07 May 2021 - 22:14

50

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When Ideal transform functor is Artinian?

Published on 25 Mar 2026 - 12:37

List Question

An artinian ring is Noetherian

A non-cyclic Artinian module has at least two distinct minimal (simple) submodule.

Commutative Artinian ring with infinitely many ideals.

Cohen structure theorem for Artinian local ring

Is $(\Bbb Q[x])_x/(\Bbb Q[x])$ an Artinian $(\Bbb Q[x])$-module?

Noetherian and Artinian quotient

Do Artin rings contain many commutative Artin subrings?

Is there exist a hollow module which is not Artinian

Show that if $P_n$ is a descending chain of submodules in $N$, then so is $f^{-1} (P_n)$ in $M$

Show that, given $f:M→N$, if M is an artinian module so is N

$A/\alpha$ is Noetherian as an $A$-module but how to get it is Noetherian as an $A/\alpha$-module?

Show that $A\simeq k[x_1,...,x_d]/I$

Zero dimensional quotient of a local Noetherian ring

Question about simple module over semisimple Artinian ring

When Ideal transform functor is Artinian?

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